Method for Calibrating a Measurement Instrument of an Optronic System

ABSTRACT

A method for calibrating measurement instruments of an optronic system in motion, with positions P 1 , P 2 , . . . , P i , . . . , comprises: a device for acquiring images of a scene comprising a fixed object G 0 ; and means for tracking the fixed object G 0  during the acquisition of these images; means for obtaining the positions P 1 , P 2 , . . . ; at least one instrument for measuring the distance and/or an instrument for measuring angles of orientation and/or of attitude between this measurement instrument and the fixed object G 0 , according to a line of sight LoS. It comprises the following steps: acquisition at instants t 1 , t 2 , . . . of at least two images, each image being acquired on the basis of different positions P 1 , P 2 , . . . of the system, the fixed object G 0  being sighted in each image, but its position being unknown; acquisition at the instants t′ 1 , t′ 2 , . . . of measurements of distance and/or of angle; synchronization of the measurements of distance and/or of angle with the positions P 1 , P 2 , . . . established at instants t 1 , t 2 , . . . ; estimation of the measurement defects which minimize the dispersion of at least two points of intersection G ij  between the LoS at the position P i  and the LoS at the position P j , as a function of said measurements and of the known positions P i , P j  of the system.

The field of the invention consist of the calibration of an optronicsystem in motion whilst viewing a fixed point for the benefit of thelocation thereof or the pointing thereof. This system is equipped withmeasurement instruments making it possible to perform measurements ofangles and/or distances of the fixed point sighted. The inventionrelates more precisely to the calibration of these measurementinstruments installed in the system.

Examples of these measurement instruments include: platform navigationsystems, sensors for scene detection and analysis and, in certaininstances, weapons to deter or assail targets in security or combatmissions.

-   -   The navigation system traditionally uses, for its positioning,        an inertial rig comprising gyrometers, accelerometers and        processing operations for the platform attitude calculation; a        GPS as well as a barometer also contribute to its positioning        and their measurements are fused with the inertial measurements,        for better quality of the general navigation solution.    -   Systems for scene detection and analysis comprise optronic        sensors with detectors operating from the visible region to the        infrared for acquiring a video of the scene, a telemeter for        measuring the distance thereto. The line of sight (or LoS) of        the sensor has an ability to orient itself with agility so as to        rapidly acquire a zone of the scene corresponding to the        instantaneous field of vision of the sensor. Inertial        measurement units or other opto-mechanical devices are further        used to measure the attitude of the LoS with respect to a        reference of the sensor or in an absolute manner.    -   Weapons systems comprise inertial and positioning means for        guiding munitions toward their objectives. They may moreover use        homing heads based on optronic imaging or radar to correct their        terminal guidance onto the designated targets.

In the conventional calibration procedures, the instruments or equipmentneed to be aligned with the reference system of the platform and theirrespective positionings need to be “harmonized”.

This optronic system is generally installed on a platform aboard anaircraft or more generally aboard a vehicle whose known position is forexample provided by an inertial rig.

The determination of the defects of mounting of the system on theplatform and of the defects of the measurements performed by theinstrument is a step prior to any location or pointing procedure, inparticular when the latter involves measurement instruments distributedover the system.

Mounting defects are manifested by a non-alignment of the reference axesof the coordinate frame of the platform with those of the coordinateframe of the measurement instrument. The operation of measuring theangles representing the transformation between coordinate frames is aprocedure dubbed harmonization, when it entails mutually orienting themeasurement instruments; or alignment when it entails orienting (orpositioning) them in relation to the reference coordinate frame of thesystem (boresight alignment).

In addition to the errors of orientation related to the reference axesof the measurements of angles (in particular demarcated by the axes ofgyrometers in inertial systems), the mounting of a sensor on a platformof airborne type introduces deviations of orientation between thereference axes of the platform and of the sensor of possibly as much asseveral degrees. A commonplace value of the errors in the knowledge ofthe mounting angles is of the order of 10 mrad.

These errors originate from the production of various hardwarecomponents such as the quartz, which regulates clocks, theaccelerometers, which measure accelerations, and demarcate thedirections of axes around which gyrometers measure angular speeds.

The attitude of the system is typically marred by an error of about 1mrad when the information arises from an inertial rig of aeronauticalclass.

Instruments for measuring angles and/or distances commonly introduce abias of a few milli-radians.

During operation, the platform and the reference axes may undergomechanical and thermal deformations in particular caused respectively bya strong acceleration or deceleration and by the variation in the flyingheight. These thermomechanical constraints induce, on the measurements,a bias of possibly as much as a few mrad.

Among measurement defects may be cited, notably, noise, biases, scalefactors and drifts. The scale factor is manifested by a deviation of themagnitude measured with respect to the true value whose value isproportional to the value of the magnitude. Its order of magnitude is afew tens of parts per million (ppm for short). The drift is manifestedby a deviation in the magnitude, which grows over time from a date atwhich the latter was corrected. One speaks of slow drift if the increaseis small in relation to the value. When the time span of themeasurements is small enough for the deviation in drift not to beimportant, it may be processed as an extra bias over the time intervalconsidered.

For the measurements of angles the specific mounting values may be ofthe order of about ten degrees whereas the aggregate of the defectsleads to residual errors of about 10 mrad. The translations between thecoordinate frames of the platform represent deviations of possibly asmuch as a few meters with residual errors, which are controlled so as tobe a few centimeters.

The parameters that we propose to estimate relate equally well to thedefect of a measurement of an apparatus pertaining to on-lineinformation as to the mounting of the equipment on the platform.

There exist several calibration schemes with variations inherent to thefield of application.

In the field of metrology, measurement is necessary for any knowledge,for any decision taking and for any action. Characterization of thedefects of measurement instruments constitutes a systematic step withinthe production of elementary instruments or sensors integrated withincomplex systems or sensors. This characterization is manifested in aconventional manner by the estimation of properties (bias, scale factor,etc.) of the physical magnitudes (angle, distance, etc.), characterizedby their statistical values (mean, standard deviation, etc.) over thefield of use of the system.

The metrology operations are generally performed on the ground on testbeds and in a very precise manner but under particular measurementconditions which cannot always reflect the real conditions of use. Thesecalibration procedures are expensive, laborious, and difficult to carryout through lack of room within the equipment; moreover the realizationon the ground of the conditions of acquisition (distance, temperature,mechanical constraint) and of modeling remains limited by the knowledgeof the phenomena.

To determine the ground alignment, the metrology operations are lengthyand consume specific means. They have moreover to be potentiallyrepeated, thus rendering them very expensive and unsuited to fast andpractical use of the instruments on mobile platforms.

Moreover, measurement instruments are subject to phenomena of temporaldrift and aging that may modify their bias. This assumes a strategy ofmaintaining operational condition (MCO), with plans regarding resumptionof testing and calibration.

In the field of industry, and for robotic applications, means arecommonly implemented to carry out the calibration of pose (position andorientation) of mechanical items or parts relating to a fixed or mobilestructure as described in the article by P. Renaud and co-authors“Optimal pose selection for vision-based kinematic calibration ofparallel mechanisms”, Proceedings of the 2003 IEE/RSJ. Conference onIntelligent Robots and Systems. Las Vegas. Nev. October 2003.

These operations traditionally consist in estimating the position andthe orientation of the mechanical part or item in relation to a fixed ormobile structure on the basis of a model.

The measured information is of high precision but often relative. Forour application, a scheme making it possible to directly evaluate theglobal orientation is sufficient and absolute information is sought.

Moreover the calibration of the systems with which we are concernedoften exhibit a significant number of joints or gimbals (see for exampleFIGS. 10, 15, 16, 17 in “Air Reconnaissance Primary Imagery DataStandard” Edition 4 of 14 Mar. 2006).

In the medical setting, in conjunction with robotics and enhancedreality, means are being developed for assisting tricky operationsrequiring accuracy of positioning in surgical interventions, asdescribed for example in T. Sielhorst T and co-authors “Advanced MedicalDisplays—A Literature Review of Augmented Reality”, J. of Displaytechnology, Vol 4 No 4 Dec. 2008

The solutions afforded in respect of the medical field cannot beproduced in a dynamic and non-cooperating setting. In theseapplications, knowledge of the setting makes it possible for example toprearrange markers or to learn certain characteristics of theenvironment so as to position and orient the equipment used. Moreoverthe information produced is often relative, whereas for the location orpointing application, absolute information is sought.

In medicine, as for the other applications mentioned, the processes arenot autonomous since they are based on reference data (considered to beexact) on the environment, or on exchanges of information in the form ofcooperation between distributed systems or on a specific intervention ofthe user.

To position an object by triangulation in the presence of bias, certainauthors such as Mangel in “Three bearing method for passivetriangulation in systems with unknown deterministic biases”, IEEE TAESVol 7 No 6 Nov. 1981, have favored schemes able to provide a solutionwhich is not too disturbed by their presence. But these approaches donot afford finer knowledge of the system so that it can be betterutilized under new conditions.

In the field of positioning and navigation, fairly recent works seek tocorrect measurement defects by using physical redundancies (duplicationof the measurement instruments) or software. These approaches relateessentially to GPS positioning and orientation systems (INS), such asdescribed by Pittelkau in “Calibration and Attitude Determination withRedundant Inertial Measurement Units”, J. of Guidance Control andDynamics. Vol. 28, No. 4, July-August 2005.

But the use of physical redundancies exhibits recurrent costs and makesit necessary to borrow existing architectures. Problems regardingbulkiness and room available within the equipment must also be takeninto account. Finally they do not make it possible to measure thealignments on all the useful gimbals for the system.

In the military field, the fusion of data entails specific needs and inparticular with the need for associating diverse data:

-   -   For multi-sensor tracking, academic works have been concerned        with the training of surveillance radar antennas on Geographic        North so as to improve the tracking of aircraft by several        radars on the scale of a country or even a continent. Within        this framework may be cited the work carried out by:        -   Li and co-authors “A real-time bias registration algorithm            for multiradar systems”, 7th International Conference on            Signal Processing (IEEE) 2004, or else,        -   Dong and co-authors “A generalized least squares            registration algorithm with Earth-centered Earth-fixed            (ECEF) coordinate system”, 3d International Conference on            Computational Electromagnetics and Its Applications            Proceedings 2004,    -   For location in the presence of angular bias, the calibration        (or boresighting) operation consists in carrying out an        adjustment which makes it possible to align the Line of Sight        (or “LoS”) on the sighting axis of the optronic system installed        on a platform.    -   For the exchange of information between distributed sensors, the        necessity for interoperability favors the development of        normalization, in the realms of positioning and of fusion        between heterogeneous sources. STANAG 5516, the acronym standing        for the expression “STANdard AGreement”, reserves specific        fields (designated by PPLI for Precise Participant Location and        Identification) to allow the exchange of the known positions        between the participants of the network for cooperative        calibration.

For applications using cooperating measurement instruments, data fusionoffers advantages in terms of autonomy and independence to theenvironment. On the other hand, they pose constraints relating to thenumber and distribution of measurement instruments and require means ofcommunication and information exchange to these instruments, as well asan identification of common objects to which the information to bereconciled pertains. This situation does not correspond to the desireduse.

Airborne measurement instruments evolve under fairly differentthermomechanical conditions from what may generally be reproduced on theground under realistic conditions with all the diversity encountered intheir area of operation.

Whatever the area of application, these locating instruments requiresystematic and periodic checking in order to manage their temporal driftand their aging.

Calibration procedures are expensive, laborious, and difficult to carryout through lack of room within the equipment; it is also difficult torealize on the ground the conditions of acquisition (distance,temperature, mechanical constraint) and of realistic modeling whichremains limited by the knowledge of the phenomena.

The aim of the invention is to remedy these drawbacks. More precisely,it entails reducing the cost of the calibration and its maintenance,while improving its precision and its stability for applications whereone seeks to improve in an autonomous and permanent manner:

-   -   the locating of non-cooperating objects on the basis of passive        measurements and/or distance measurements    -   the pointing of the sensor on the basis of measurements of        angles.

The subject of the invention is a method for calibrating measurementinstruments of an optronic system in motion, with positions P₁, P₂, . .. , P_(i), . . . , this optronic system comprising:

-   -   a device for acquiring images of a scene comprising a fixed        object G₀, and    -   means for tracking the fixed object G₀ during the acquisition of        these images,    -   means for obtaining the positions P₁, P₂, . . .    -   at least one instrument for measuring the distance and/or one        instrument for measuring angles of orientation and/or of        attitude between this measurement instrument and the fixed        object G₀, according to a Line of Sight (LoS),        It is principally characterized in that it comprises the        following steps:    -   acquisition at instants t₁, t₂, . . . of at least two images,        each image being acquired on the basis of different positions        P₁, P₂, . . . of the system, the fixed object G₀ being sighted        in each image, but its position being unknown,    -   acquisition at the instants t′₁, t′₂, . . . of measurements of        distance and/or of angle,    -   synchronization of the measurements of distance and/or of angle        with the positions P₁, P₂, . . . established at instants t₁, t₂,        . . . ,    -   estimation of the measurement defects which minimize the        dispersion of at least two points of intersection G_(ij) between        the LoS at the position P_(i) and the LoS at the position P_(j),        as a function of said measurements and of the known positions        P_(i), P_(j) of the system.

This method makes it possible to carry out autonomous calibration(without resorting to an external action or information), in-situ (underoperational conditions), or within the operational setting, byevaluating the values obtained under the conditions of use, thusrepresenting an advantage in respect of the calibration need of airborneoptronic systems.

In regard to applications of ground metrology or cooperative calibrationbased on a network, the novelty of the proposed approach is that itoperates on the basis of a single measurement instrument, in anautomatic and autonomous manner, without requiring human intervention orexact knowledge about the context of acquisition.

According to a characteristic of the invention, the sole calibratedmeasurement instrument is an instrument for measuring angles oforientation and/or of attitude; the measurements are then acquired onthe basis of at least three different positions P₁, P₂, P₃.

According to another characteristic of the invention, the solecalibrated measurement instrument is a telemeter, and the measurementsare acquired on the basis of at least two different positions.

When at least one other fixed object G₁ is visible on at least twoimages, it optionally furthermore comprises a step of matching betweeneach image of the fixed objects G₀, G₁, the step of calculating themeasurement defects furthermore being carried out as a function ofpredetermined characteristics or parameters internal to the sensor (suchas the size and the dimensions of the elements of the photo-sensitivematrix, the focal length, the Image Principal Point, the opticaldistortion). Note that with sufficient available measurements, thesemagnitudes can also be estimated by linearizing the picture-takingequations of the sensor around the approximate values. Moreover some ofthese parameters, such as the focal length and the distortion, fluctuatemore particularly with temperature.

Preferably, it comprises a step of calculating the geographical positionof G₀ and optionally of the other fixed objects, on the basis of thecalibrated measurements.

According to a variant, it comprises a step of pointing at the fixedobject G₀.

According to a characteristic of the invention, it comprises a step ofoptimizing the measurement conditions, which is based on thedetermination of an optimal trajectory of the sensor for a knownposition of the object G₀, or on the determination of a zone to befavored for the search for the object G₀.

According to another characteristic of the invention, it comprises astep consisting in applying the calculated defects to the measurements.

This method exhibits numerous advantages since it improves:

-   -   the performance of direct geo-referencing of the image, thereby        allowing better location of all its points,    -   the absolute pointing of the LoS, thus making it possible in        particular to place an object of known coordinates as close as        possible to the center of an image and thereby even to reduce        the lags in respect of its acquisition and its analysis.

Furthermore:

-   -   it is autonomous, requiring neither intervention or monitoring        of the operator, nor reference data on the environment,    -   it operates in a commonplace mode of use of measurement        instruments,    -   it does not require any complex trajectory of the platform to        afford utilizable performance,    -   it appreciably relaxes the requirements on the precision of        pointing of the LoS which have to be allocated during the        specification of the system,    -   it lightens the metrological need aimed at the grading of the        ground boresighting and thus avoids difficult ground procedures        that would be lengthy and expensive and that would have to be        repeated.

The subject of the invention is also an optronic system able to bedisplaced, which comprises:

-   -   a device for acquiring images of a scene comprising a fixed        object G₀,    -   means for tracking the fixed object G₀ during the acquisition of        these images,    -   means for obtaining the positions P₁, P₂, . . .    -   at least one instrument for measuring the distance and/or one        instrument for measuring angles of orientation and/or of        attitude between this measurement instrument and the fixed        object G₀, according to a line of sight.        It is characterized in that it comprises means for implementing        the method as previously described.

The calibration and alignment procedures correspond to the term“registration” in certain fields. In the world of image processing, onecommonly speaks of “registration of images”, which corresponds to theaction making it possible to superimpose the contents of several imagesfor example.

Other characteristics and advantages of the invention will becomeapparent on reading the detailed description which follows, given by wayof nonlimiting example and with reference to the appended drawings inwhich:

FIG. 1 schematically illustrates the dispersion of erroneous positionsobtained on the basis of four different positions,

FIG. 2 schematically represents an exemplary optronic system equippedwith means for calibrating a measurement instrument,

FIG. 3 schematically represents the axes of the coordinate frame of thesystem and those of the coordinate frame of the measurement instrument,

FIG. 4 schematically represents a simple configuration of measurementsfor a calibration process (A(L)RFM) for bias and scale factor like angleand distance measurement defect,

FIG. 5 represents a diagram of the measurements logged to feed themethod according to the invention,

FIG. 6 shows diagrammatically the transformations for passing from onecoordinate frame to the other,

FIG. 7 present a diagram of the acquisition conditions allowingsimultaneous passive location and calibration by using the motion and byproceeding either solely with passive measurements (FIG. 7 a), or byadding active or distance measurements (FIG. 7 b).

Across the figures, the same elements are tagged by the same references.

The optronic system of interest comprises:

-   -   a platform making it possible to carry out the displacement of        the system, the measurement of its positioning and the mounting        of the optronic sensor,    -   an optronic sensor constituting the instrument making it        possible to image and sight a fixed point on the ground G₀ on        which measurements of angles and/or of distances are carried        out.

Hereinafter a system installed aboard an aircraft will be taken asexample, but it could equally well be installed in a robot or aterrestrial platform or even be carried directly by a user. The term“platform” is therefore used in its most generic form.

The method according to the invention rests upon:

-   -   the displacement of the optronic system over time;    -   the means for acquiring a fixed point of interest (or object)        G₀;

The means for acquiring a fixed point cover the determination of anappropriate zone of the scene, the choice of a relevant object and itstemporal tracking. This tracking may be manual or automatic. The abilityfor automatic tracking of the object consists in keeping it maintainedat the center of the image during the displacement of the system overtime (that is to say in the course of the sequence of images acquired bythe sensor). This is carried out by measuring its apparent displacement(deviometry) between a reference image and the current image. In orderfor this displacement measurement to be possible, it is necessary forthe object to have been “locked onto” beforehand, that is to saydetected and located in the image. Lock-on allows automaticinitialization of tracking.

-   -   means for acquiring successive images of a zone comprising this        fixed point G₀,    -   the measurement of angles and/or distances between the        measurement instrument and the object sighted G₀;    -   the knowledge of the absolute coordinates of the positions P_(i)        of the system at the measurement instants;    -   a processing of the successive measurements to make it possible        to estimate the best values of defect allowing for the        immobility of the point sighted G₀.    -   a small variation of the parameters to be calibrated on the        scale of the duration of gathering of the measurements useful        for their estimation.    -   means for measuring the thermodynamic magnitudes on the most        sensitive measurement components (temperature for example) so as        to allow a temporal analysis of the behavior according to        various operating conditions and to forecast during use the a        priori values of the parameters to be estimated according to the        values learnt from the previous calibration procedures.

When the system is considered to be in “tracking mode” pursuing anobject of the scene this signifies that its position (or its pixelcoordinates) in the image is kept constant during the acquisitions. Inthe most frequent case, the tracking mode makes it possible during thedisplacement to keep the object G₀ at the center of the images of thesequence constituting the optronic video. The less frequent case oftracking with respect to the fixed object, imaged outside of the imagecenter, also makes it possible to carry out the process.

The measurements grade the picture-taking parameters of the imageacquisition device.

The proposed scheme subjects the positions G_(ij) obtained by the set ofmeasurements acquired over time, to the constraint of positioning afixed point G₀ for the various positions P₁, P₂, . . . , of the optronicsystem.

Instrument mounting or/and measurement defects in fact produce positionsolutions for the fixed object G₀ that differ from one another as wellas from reality. With each position P_(i) of the system are associatedthe measurements taken at these positions: this is designated themeasurement ensemble. The N measurement ensembles (position of thesystem, angle and/or distance) provide N positions, which on account ofthe measurement errors do not coincide at a single point but exhibitdispersion. The dispersion between the measurements constitutes asignature of the defects for given picture-taking conditions (trajectoryof the system, angles considered, thermodynamic operating condition).This is illustrated in FIG. 1 with measurements of angles about a singledirection; represented in this figure are four known positions P₁, P₂,P₃, P₄ of the platform, as well as the real position G₀ of the fixedobject. The measurement defect introduces an error Δθ in the LoS of themeasurement instrument, θ being the angle of rotation in the plane asillustrated in FIG. 3. If the LoSs were perfectly aligned, they wouldall cross at G₀. In fact, they cross at several dispersed points. TheLoS arising from P₁ crosses at G₁₂ with the LoS arising from P₂, at G₁₃with the LoS arising from P₃, at G₁₄ with the LoS arising from P₄.Likewise, the LoS arising from P₂ crosses in G₂₃ with the LoS arisingfrom P3, at G₂₄ with the LoS arising from P₄. Finally, the LoS arisingfrom P₃ crosses at G₃₄ with the LoS arising from P₄. On the basis of Nmeasurements (one ensemble of measurements per position P) it is thuspossible to construct N(N−1)/2 positions whose distribution signs themeasurement defects Δθ as illustrated in the example hereinabove for onedimension.

By generalizing to three dimensions, the angle of rotation of the imageabout the direction of pointing of the LoS is considered in addition tothe two angles characterizing the said direction. The mechanization(assembling) of the various sensors on the platform leads to theconsideration of various coordinate frames, whose axes and origins aredistributed within the system, such as notably:

-   -   the antenna of the receiver of the GPS,    -   the inertial navigation rig (CNI) of the platform,    -   the image principal point (PPI) or optical center of the imager.        The passage from each of these coordinate frames to the others        is described by a transformation of the (Translation and        Rotation) type.

The physical modeling of the various gimbals of the system is conductedaccording to the analysis of the effects of the contributions induced bythe errors of translations (gaps between axes) and of rotation(alignments of axes) as well as of the order of the residual errors thatone seeks to determine. This analysis conditions the fineness of themodeling to be adopted for a piece of equipment and a given need. Thefeeding of the process of estimation, by the extraction of imagefeatures of several views corresponding to details of fixed elements inthe scene, affords a significant number of measurements. Thissignificant quantity makes it possible to envisage the estimation of ahigh number of calibration unknowns provided that the pairing quality,the distribution and the dilution (or geometry of the viewing conditionsVC) of the features are sufficient and that the various transformationsto be characterized are properly separable. FIG. 6 illustrates such asituation where the rotation “R” and the translation “T” are expressedas a function of the elementary transformations (R_(k), T_(k)) betweenthe successive coordinate frames as:

$\begin{matrix}{R = {\prod\limits_{k = 1}^{K}\; R_{k}}} & \left( {{equation}\mspace{14mu} 1} \right) \\{T = {\sum\limits_{k = 1}^{K}{\left( {\prod\limits_{n = 1}^{K - 1}\; R_{n}} \right)T_{k}}}} & \;\end{matrix}$

When the transformations are known to first order, we seek linearsolutions to this system in the form:

R _(k) =R _(1k) ·R _(ε)

T _(k) =T _(1k) +T _(τ)

where the elementary rotation matrix R_(ε) and the elementarytranslation T_(τ) are respectively denoted:

$R_{ɛ} = \begin{pmatrix}0 & {- ɛ_{Z}} & ɛ_{Y} \\ɛ_{Z} & 0 & {- ɛ_{X}} \\{- ɛ_{Y}} & ɛ_{X} & 0\end{pmatrix}$ $T_{\tau} = \begin{pmatrix}\tau_{X} & \tau_{Y} & \tau_{Z}\end{pmatrix}^{T}$

To estimate the elements of an elementary rotation that are placed at acertain rank in (equation 1), the terms situated on their “right” of therotation in the equation are written in the form of a vector U=(u1, u2,u3)^(T). Writing it this way makes it possible to simply obtain thesought-after elements of the rotation by transforming the productR_(ε)·U into:

${R_{ɛ}U} = {\begin{pmatrix}0 & u_{3} & {- u_{2}} \\{- u_{3}} & 0 & u_{1} \\u_{2} & {- u_{1}} & 0\end{pmatrix}\begin{pmatrix}ɛ_{X} \\ɛ_{Y} \\ɛ_{Z}\end{pmatrix}}$

Knowledge of the transformations can originate either fromspecifications, evaluations or ground calibration for example or on thebasis of previous evaluations carried out with various operatingconditions of the system.

The number of magnitudes to be estimated is conditioned by the type ofhardware architecture of the instrument, which is used for themeasurement of angles of attitude. This number quickly becomessignificant with the increase in the number of mechanical gimbals to becompounded to get the absolute attitude of the line of sight or “LoS”.The attitude calculation uses 3K angles for a mounting of the systeminvolving relative measurements of attitude between K mechanicalgimbals.

Thus it will not be sought to estimate the orientation contributionsthat are liable to occur at the level of each mechanical gimbal sincethere may rapidly be a large number of them. The chaining together of 2pure rotations between 2 gimbals (or coordinate frames), for example, isstrictly equivalent to a single rotation and the estimation of theglobal rotation does not make it possible to separate the information toallot one of them at the level of the contributions of each gimbal. Inthe case of a mounting or of a configuration where the attitudemeasurement bias may be considered to be added directly to that of themounting, a scheme making it possible to directly evaluate the globalorientation may be sufficient to globally characterize the defects ofbias (mounting+measurements). The application of the global correctionto one of the gimbals will fulfill the sought-after objective in favorof the location or pointing functions.

The attitude calculation may typically be reduced to a minimum of 3elementary rotations for a measurement instrument, which estimates theabsolute attitude of its LoS by means of an AHRS device, the acronymstanding for the expression “Attitude Heading Reference System”.

Hereafter, we consider a system for which the chaining together of thesetransformations amounts to a rotation “R” and translation “T”transformation which generally makes it possible to express thecoordinates of a point in the final coordinate frame as a function ofits coordinates in the initial coordinate frame as:

(OM)_(N) =R(OM)₁ +T

The description of the proposed process thus adopts a modeling of thebiases of angle and of position by this transformation with 6parameters, although it is possible to enter into the details of a morecomplex specific mechanization for a given system configuration.

The modeling of the picture-taking function for an image i of theoptronic sensor situated at (x_(i), y_(i), z_(i)) makes it possible towrite generally the location function allotting position coordinates (x,y, z) in a geographical coordinate frame associated with the scene to apoint k with coordinates (p_(ki), g_(ki)) in a coordinate frame of theimage “i” in the form:

$\begin{pmatrix}x & y & z\end{pmatrix}^{T} = {G\left( {\Theta_{i},p_{ki},q_{ki}} \right)}$$\begin{pmatrix}{x_{i} - x} \\{y_{i} - y} \\{z_{i} - z}\end{pmatrix} = {\mu_{k}{R\begin{pmatrix}{p_{k} - p_{0}} \\{q_{k} - q_{0}} \\{- f_{0}}\end{pmatrix}}}$

In addition to the elements (p₀, g₀, f₀), the internal parameters modelthe principal effect of the distortion in the form of a radialdeformation of the perfect pixel coordinates (p,q) by transforming theminto (p′,q′) according to the following form:

p′=p _(c) +L(r)(p−p _(c))

q′=q _(cx) +L(r)(q−q _(c))

r=√{square root over ((p−p _(c))²+(q−q _(c))²)}{square root over ((p−p_(c))²+(q−q _(c))²)}

In this expression, (p_(ki),q_(ki)) are the image coordinates of thepoint k in the image i, and (x, y, z) the coordinate of thecorresponding point on the ground. The transpose of the vector u isdenoted u^(T)—and the vector Θ contains at one and the same time (seeFIG. 5):

-   -   the internal picture-taking parameters (focal length, position        of the Image Principal Point (PPI) on the detector, optical        distortion),    -   the external picture-taking parameters varying at each image        “i”: position of the P_(i) of the sensor with coordinates        (x_(i), y_(i), z_(i)) and the attitude (ψ_(i), θ_(i), φ_(i)) of        the image in the scene coordinate frame,    -   the calibration parameters (τ_(x), τ_(y), τ_(z), ε_(x), ε_(y),        ε_(z)) common to the various images,    -   optionally the distance between the PPI and the point of the        scene corresponding to the image center if a telemeter        harmonized with the optical axis is available.    -   the pixel with coordinates (p_(c), q_(c)) corresponds to the        center of the distortion also called the Principal Point of        Symmetry (PPS).

It is noted that the internal parameters of the system are assumed notto vary from one image to the other during the measurements acquisitionphase.

The proposed calibration process has following characteristics:

-   -   automatic management makes it possible to select the sighted        zone so as to decide on an effective implementation of the        process according to:        -   i. the analysis of the content of the scene based on the            contrast of the imaged zone and on the characteristics of            the features extracted by the image processing,        -   ii. the performance level that has to be obtained so as to            ensure required location or pointing performance based on a            given configuration of trajectory (example for an            aeronautical platform navigating under a flight plan or for            a terrestrial platform following a transport network). In            this approach, the observation zone is made to vary on a            partition of the scene of the order of the imaged size and            the performance of the calibration attainable is summarized            by pointing at the center of this zone. The performance is            obtained through the Fisher Information Matrix (FIM), the            expression for which is described a little further on            (equation 2), by sampling the trajectory at the rate of the            measurements. The zone of best performance attainable by the            sensor is thereafter retained for the acquisitions,        -   iii. the need to propose a trajectory for the system or to            evaluate the best achievable performance by means of an            ideal estimation technique; accordingly, it is proposed to            determine an optimal geometric configuration (according to a            subsequent description of optimization based on the FIM).    -   an image sequence,    -   a mode of tracking with lock-on to a fixed point of the scene        appearing as contrasted in the image,    -   the search for contrasted features in the image “i”, by        extracting points of interest with coordinates (p_(ki), q_(ki)        for k=1 . . . K_(i)), such as corners, blobs, . . . or by more        robust descriptors based on the algorithms such as SIFT or SURF        (derived respectively from the expressions Scale-Invariant        Feature Transform and Speeded Up Robust Features),    -   the Matching of the previous image features (MIF for Matched        Images Feature) by utilizing the epipolar geometry of the images        for the MIF between images taken from fairly distant positions        or more conventional techniques for tracking in the image        sequence. A pairing (or MIF), of features (denoted k and l)        between the images (denoted i and j) gives rise to a link of        features in the form of a pair {(p_(ki), q_(ki)); (p_(lj),        q_(lj))}. Links in the form of a triplet or quadruplet of        features can also be used when they are detected between 3 or 4        images for example,    -   the estimation of the parameters which may consist in all or        part:        -   i. of the picture-taking and calibration parameters over the            sequence.        -   ii. of the coordinates of the points G_(m) on the ground            corresponding to the matched features.        -   iii. of the parameters internal to the sensor (such as focal            length, and distortion) insofar as the observations are            sufficiently dense over the image and varied in terms of VC            as to allow their estimation under correct conditions of            observability.

The estimation of the parameters is conducted so as to minimize the setof the residuals on the ground coordinates of the matched featuresextracted from the sequence.

In practice, the minimum number of features to be used depends on thenumber of parameters to be estimated. Each pair of features gives aminimum of 2 observation equations and more if the object associatedwith the features is visible on more than 2 images. These pairs arise ingeneral in significant number on account of the contrasted detailscontained in the scene and of the significant overlap between theimages.

The process exhibits an advantage in regard to autonomy on account ofits ability:

-   -   to operate without using any landmark point,    -   to lock on and automatically track the point sighted by virtue        of the agility of the LoS and its coupling to the deviometry        processing,    -   to extract and to pair in a robust manner the features between        the images,    -   to telemeter automatically on the point corresponding to the        image center.        The process also exhibits a performance advantage which rests        upon the quality of the estimation consisting:    -   in controlling the coherence of the optronic information through        the local coherence of the detector and of the geometry of the        picture shots taken,    -   in using the telemeter, when the latter may be used, to link the        position of the sensor to the scene on the basis of measurements        of highly accurate date-stamps (the position of the sensor        through the date-stamps of the GPS and the measurement of        distance to the scene through the measurement of flight times).

In space, the LoS arising from a point P_(i) does not cross the LoSarising from a point P_(j) on account of the measurement errors.Hereinafter, the middle of the segment which minimizes the distancebetween the LoS arising from P_(i) and the LoS arising from P_(j) iscalled the point of intersection G_(ij).

At least two points G_(ij) are required in order to allow a firstdetermination of these defects, i.e. at least 3 ensembles of two anglemeasurements or 2 ensembles of 3 measurements, one of which is adistance measurement. For these 2 configurations, we therefore have atleast 6 measurements: {(θ₁, φ₁), (θ₂, φ₂), (θ₃, φ₃)} in passive mode or{(θ₁, φ₁, ρ₁), (θ₂, φ₂, ρ₂)} in active mode, where ρ_(i) represents themeasurement of distance between G₀ and the measurement instrument(typically a telemeter) considered at the position P_(i). Of course, themore points G_(ij) that are available and the greater their dispersionin space, the more precise the estimation of the error.

The presence of the telemeter is optional since the process is capableof operating on the basis of angular measurements alone. Its presencemakes it possible to increase the information gathered and to improveperformance.

It is possible conversely to have only distance measurements “ρ”obtained with a telemeter harmonized angularly with the axis of the LoS;an error Δρ in the measurement of the telemeter is then measured.

This configuration exhibits the advantage of operating with no componentfor inertial measurements, thus on the one hand reducing the hardwarecost for the system and on the other hand reducing the constraintsrelated to the characteristics of these measurements such as drift,integration constant, integration of noise, etc.

The use of a telemeter (alone or with inertial means) presupposes aharmonization of its axis with that of the image. In the converse case,the proposed procedure makes it possible to estimate the alignment ofthe laser axis with the image axis. The proposed field of applicationmay be extended by considering that the distance measurements, which arededuced from a propagation time measurement, may be provided byinstruments other than a telemeter, such as for example a radar or asonar.

The measurements used in the method according to the invention may beeither passive, or active, or both.

The measurements of angles are for example provided by inertial meanssuch as an inertial rig, or a magnetic compass or else on the basis ofquasi-fixed references such as landmarks in space (stars, planets,satellites) etc.: these are passive measurements. It is recalled thatthe proposed principle rests upon autonomy of the system in relation tothe external data; it is thus considered:

-   -   as acceptable to point the imager so as to acquire celestial        bodies (stars, planets, satellites), and to pair them with        onboard information capable of covering the entire theater of        use of the sensor. In this case, the optronic sensor has a star        sight function including the ability to detect the centers of        the bodies (star camera function) and their identification (star        tracker function).    -   as constraining to carry onboard information of ortho-image        type, arising from a mission preparation, which exhibits a        resolution of the order of magnitude of that of the sensor with        a spatial coverage corresponding to all the zones over which the        sensor is able to operate. The constraints pertain here to the        standpoint of the data to be deployed, of the operations of        robust pairing to be carried out and of the volume of the        information and operations to be processed.

Depending on the use made of the observation equations, it is possible:

-   -   either to estimate solely the measurement defects, and one        speaks of “Calibration Through Motion” or “Registration From        Motion” (RFM),    -   or to simultaneously estimate the measurement defects and the        position of the point sighted (by compensating the measurement        errors via the estimated defects), and one speaks of        “calibration and location through motion” or “Localization and        Registration From Motion” (LRFM).

These two variants may be carried out on the basis of Passivemeasurements (PRFM/PLRFM), or Active measurements (ARFM/ALRFM). Theso-called active variants can also use passive measurements. Thus, wedesignate by PLRFM (for Passive Localization and Registration FromMotion) an application using passive measurements to estimate thecalibration parameters through the motion of the sensor (see FIG. 7 b).In the case where a distance measurement is added, the application isdesignated by ALRFM (for Active LRFM) (see FIG. 7 a).

Examples of uses of the observation equations will now be given forvarious applications.

-   -   Application (1): ARFM for the instrument calibration of a        terrestrial sensor with in particular:        -   i. the angular bias corresponding to the ignorance of the            mounting and of the declination used by a magnetic compass            and the distance bias of the telemeter,        -   ii. the scale factors on the angle and distance measurement.    -   Application (2): ALRFM for the calibration of a direction while        airborne with the calculation of bias in the angular direction        and the distance measurement of the telemeter.    -   Application (3): Location and calibration on the basis of        measurements of positions and of distances alone.    -   Application (4): calibration and georeferencing of images by        aero-lateration.

Two other aspects of implementation of the process are thereafterpresented aimed at:

-   -   the automation of its operation and the optimization of the        conditions of information gathering,    -   the consideration of the variability of the estimated parameters        according to the (thermomechanical) operating conditions.

Application (1): Calibration of Instruments on a Terrestrial Sensor

For terrestrial applications, optronic systems generally offer locationof the sighted object of the scene, placed at the center of the image.This is carried out on the basis of a camera comprising a GPS receiverfor determining the position of the sensor, a telemeter for measuringthe distance to the object and an LoS orientation measurement means.Orientation measurement traditionally relies on a magnetic compass (DMC,the acronym standing for the expression “Digital Magnetic Compass”). Theobtaining of a geographical position of good performance constitutes agenuine challenge since the DMCs, which are used because of their lowcost and small bulk, exhibit the following drawbacks:

-   -   the intrinsic performance of the measurement is moderate (the        precision is of the order of 0.5°)    -   the accuracy of alignment of axis of the DMC and of the image is        limited so as to maintain manufacturing complexity consistent        with the volume of the run and the cost of the equipment.    -   The orientation measurement is carried out with reference to the        geomagnetic meridian, which locally exhibits a deviation of        orientation (declination) with regard to geographical North.        This declination value may be obtained according to information        of geographical maps or geomagnetic models (such as the IGRF for        International Geomagnetic Reference Field or the WMM for World        Magnetic Model). These models rely on the series expansion of        the potential of the geomagnetic field in the form of a product        of coefficients and of basis functions using spherical        harmonics. They allow the calculation of the amplitude as well        as direction of the local magnetic field on the basis of the        coefficients tabulated in published reference versions. Every 5        years, the IGRF thus becomes the DGRF (with “D” for Definitive        GRF) with data available over the period 1900-2010. Whichever        magnetic field model is used, the orientation of the field must        be on the one hand extrapolated with regard to the current date        of the measurement and on the other hand remains able to vary        locally with a shorter spatial frequency than that corresponding        to the resolution of the models. The deviation between the value        obtained by the model and that actually realized at the level of        the measurement site is manifested essentially by a systematic        error or angular bias.

For these various reasons, the proposed procedure exhibits particularinterest since it makes it possible to obtain in a simple and analyticalmanner the biases of angular and distance measurement. Accordingly, ituses:

-   -   a displacement over the terrain around a fixed object,    -   a minimum of 2 ensembles of measurements on the object, one        ensemble comprising the position of the sensor, its distance        from the object, its azimuth.

In the presence of a defect of bias type in regard to the angle anddistance measurements, a point with position (x₀, y₀) may be directlylocated from a position (x_(k), y_(k)), according to ideal measurements:

x ₀ =x _(k)+ρ_(k) cos θ_(k)

y ₀ =y _(k)+ρ_(k) sin θ_(k)

In the presence of bias in the measurements of angle and distance:

θ_(kb)=θ_(k)+Δ_(θ)

ρ_(kb)=ρ_(k)+Δ_(ρ)

the point situated at the (true) position with coordinates (x₀, y₀) andobtained at the position (x_(b), y_(b)) given by:

x _(b) =x _(k)+ρ_(kb) cos θ_(kb) =x _(k)+(ρ_(k)+Δ_(ρ))cos(θ_(k)+Δ_(θ))

y _(b) =y _(k)+ρ_(kb) sin θ_(kb) =y _(k)+(ρ_(k)+Δ_(ρ))sin(θ_(k)+Δ_(θ))

is, on neglecting the second-order terms:

x _(b) ≈x _(k)+ρ_(k) cos θ_(k)−Δ_(θ)ρ_(k) sin θ_(k)+Δ_(ρ) cos θ_(k)+O(Δ²)=x ₀−Δ_(θ)ρ_(k) sin θ_(k)+Δ_(ρ) cos θ_(k) +O(Δ²)

y _(b) ≈y _(k)+ρ_(k) sin θ_(k)+Δ_(θ)ρ_(k) cos θ_(k)Δ_(ρ) sin θ_(k)+O(Δ²)=y ₀+Δ_(θ)ρ_(k) cos θ_(k)+Δ_(ρ) sin θ_(k) +O(Δ²)

In the following matrix form, the above expression shows that thedisplacement corresponds, to first order, to a rotation of the biasvector with component (Δ_(ρ), ρ_(k), Δ_(θ))^(T):

$\begin{pmatrix}x_{b} \\y_{b}\end{pmatrix} = {\begin{pmatrix}x_{0} \\y_{0}\end{pmatrix} + {\begin{pmatrix}{\cos \; \theta_{k}} & {{- \sin}\; \theta_{k}} \\{\sin \; \theta_{k}} & {\cos \; \theta_{k}}\end{pmatrix}\begin{pmatrix}\Delta_{\rho} \\{\rho_{k}\; \Delta_{\theta}}\end{pmatrix}} + {\begin{pmatrix}1 \\1\end{pmatrix}{O\left( b^{2} \right)}}}$

This expression simply conveys the contribution of the two biases to apositioning (FIG. 4).A single measurement obviously does not make it possible to determine atone and the same time the position of the point and the angle bias anddistance bias. On the other hand two measurements on the same point aresufficient, by differencing, to determine the biases in the followingmanner:

${\begin{pmatrix}{{{- \rho_{k}}\; \sin \; \theta_{k}} + {\rho_{j}\; \sin \; \theta_{j}}} & {{\cos \; \theta_{k}} - {\cos \; \theta_{j}}} \\{{\rho_{k}\; \cos \; \theta_{k}} - {\rho_{j}\; \cos \; \theta_{j}}} & {{\sin \; \theta_{k}} - {\sin \; \theta_{j}}}\end{pmatrix}\begin{pmatrix}\Delta_{\theta} \\\Delta_{\rho}\end{pmatrix}} = {\begin{pmatrix}{x_{j} + {\rho_{j}\cos \; \theta_{j}} - x_{k} - {\rho_{k}\cos \; \theta_{k}}} \\{y_{j} + {\rho_{j}\; \sin \; \theta_{j}} - y_{k} - {\rho_{k}\; \sin \; \theta_{k}}}\end{pmatrix} + {\begin{pmatrix}1 \\1\end{pmatrix}ɛ_{jk}}}$

For a measurement pair (j, k), the expressions for the biases may beobtained in an analytical manner. The determinant of the system equals:

$\delta = {{\left( {\rho_{k} + \rho_{j}} \right)\left\lbrack {{\cos \left( {\theta_{k} - \theta_{j}} \right)} - 1} \right\rbrack} = {{- 2}\left( {\rho_{j} + \rho_{i}} \right)\; {\sin^{2}\left( \frac{\theta_{k} - \theta_{j}}{2} \right)}}}$

and the expressions for the biases of angle and distance are obtained,under the observability conditions (δ non-zero), according to:

Δ_(θ)×δ=(x _(j) −x _(k))(sin θ_(k)−sin θ_(j))−(y _(j) −y _(k))(cosθ_(k)−cos θ_(j))+(ρ_(j)−ρ_(k))sin(θ_(k)−θ_(j))

for the distance bias and for the angular bias by:

Δ_(d)×δ=(x _(j) −x _(k))(ρ_(j) cos θ_(j)−ρ_(k) cos θ_(k))+(y _(j) −y_(k))(ρ_(j) sin θ_(j)−ρ_(k) sin θ_(k))−2ρ_(j)ρ_(k)cos(θ_(k)−θ_(j))+ρ_(j) ²+ρ_(k) ²

The above system has a physical solution when its discriminant δ isdifferent from zero; it is moreover noted that the latter:

-   -   approaches zero when θ_(k)≈θ_(j). Stated otherwise a small        displacement of the sensor between two measurements        corresponding to a poor configuration,    -   is extremal (of value −2) when θ_(k)≈θ_(j)+π on the one hand and        that on the other hand the distances to the points are large.        This corresponds to sightings of opposite directions at a large        distance from the point.

Thus, the conditions in which calibration is optimal are opposite fromthe conditions for which location is ideal. To be effective, calibrationrequires a sensitivity to error which accordingly must be large whereaslocation needs to be insensitive thereto.

To improve performance in the presence of angular measurement error itis necessary:

-   -   on the one hand to avoid locating a point on the basis of        sightings of opposite directions, and,    -   on the other hand, to try to approach thereto so as to decrease        the sensitivity to angular errors.        -   This duality between location and calibration is not limited            to performance nor specific to this application.

In the presence of bias and scale factor type defects, in the angle anddistance measurements, the measurements are written thus:

θ_(kbf)=(1+f _(θ))θ_(k)+Δ_(θ)

ρ_(kbf)=(1+f _(ρ))ρ_(k)+Δ_(ρ)

x _(bf) =x _(k)+ρ_(kbf) cos θ_(kbf) =x _(k)+(└1+f_(ρ)┘ρ_(k)+Δ_(ρ))cos([1+f _(θ)]θ_(k)+Δ_(θ))

y _(bf) =y _(k)+ρ_(kbf) sin θ_(kbf) =y _(k)+([1+f_(ρ)]ρ_(k)+Δ_(ρ))sin([1+f _(θ)]θ_(k)+Δ_(θ))

i.e. an expression for the location to first order of the form:

x_(bf) ≈ x_(b) − f_(θ)θ_(k)ρ_(k) sin  θ_(k) + f_(ρ)ρ_(k) cos  θ_(k)${y_{bf} \approx {y_{b} + {f_{\theta}\theta_{k}\rho_{k}\; \cos \; \theta_{k}} + {f_{\rho}\rho_{k}\; \sin \; {\theta_{k}\begin{pmatrix}{{{- \rho_{k}}\; \sin \; \theta_{k}} + {\rho_{j}\; \sin \; \theta_{j}}} & {{\cos \; \theta_{k}} - {\cos \; \theta_{j}}} & {{{- \theta_{k}}\rho_{k}\; \sin \; \theta_{k}} + {\theta_{j}\rho_{j}\; \sin \; \theta_{j}}} & {{\rho_{k}\; \cos \; \theta_{k}} - {\rho_{j}\; \cos \; \theta_{j}}} \\{{\rho_{k}\; \cos \; \theta_{k}} - {\rho_{j}\; \cos \; \theta_{j}}} & {{\sin \; \theta_{k}} - {\sin \; \theta_{j}}} & {{\theta_{k}\rho_{k}\; \cos \; \theta_{k}} - {\theta_{j}\rho_{j}\; \cos \; \theta_{j}}} & {{\rho_{k}\; \sin \; \theta_{k}} - {\rho_{j}\; \sin \; \theta_{j}}}\end{pmatrix}}\begin{pmatrix}\Delta_{\theta} \\\Delta_{\rho} \\f_{\theta} \\f_{\rho}\end{pmatrix}}}} = {\begin{pmatrix}{x_{j} + {\rho_{j}\; \cos \; \theta_{j}} - x_{k} - {\rho_{k}\; \cos \; \theta_{k}}} \\{y_{j} + {\rho_{j}\; \sin \; \theta_{j}} - y_{k} - {\rho_{k}\; \sin \; \theta_{k}}}\end{pmatrix} + {\begin{pmatrix}1 \\1\end{pmatrix}ɛ_{jk}}}$

To first order, the estimate may be written as a function of themeasurement:

$\theta_{k} = {\frac{\theta_{kbf} - \Delta_{\theta}}{1 + f_{\theta}} \approx {{\left( {1 - f_{\theta}} \right)\theta_{kbf}} - \Delta_{\theta}}}$$\rho_{k} = {\frac{\rho_{kbf} - \Delta_{\rho}}{1 + f_{\rho}} \approx {{\left( {1 - f_{\rho}} \right)\rho_{kbf}} - \Delta_{\rho}}}$

Note that in 3D, this 1D situation is approached in the cases:

-   -   of long-range lateral sighting of the object and small height        from the ground,    -   of vertical sighting while advancing on the point of interest.

This approach is simply generalized in 3D, with analytical expressionsthat are longer to be expanded. In N=2 or 3 (N being the number ofdimensions), two ensembles of measurements make it possible to write 2×Nrelations and by differences, N relations make it possible to determinethe N biases in each type of measurement (Δρ, Δθ) in 2D, supplementedwith Δφ in 3D.

The correction values for the biased measurements are thereafterobtained by adding the opposite of the biases obtained to the values ofthe biased measurements. Thus, the position of the point G(x,y) sightedis obtained according to:

x=x _(k)+(ρ_(m)−Δρ)cos(θ_(m)−Δθ)

y=y _(k)+(ρ_(m)−Δρ)sin(θ_(m)−Δθ)

In the presence of biases alone, for example for the two pairs ofconfigurations of the following table, corresponding to an object G₀situated at [0,0], with the presence of a bias of −1° in the measurementDMC and of 5 m in the distance measurement, we obtain an estimation ofbias:

-   -   in the distance to within better than 1 m,    -   in the azimuth to within 5 μrad.

P_(k) [x_(k), y_(k)] (m, m) Distance ρ_(k) (m) Angle θ_(k) (°) [−5000,2500] 5590.2 −26.6  [2500, 2500] 3535.5 −135

Application (2): Location and Calibration on the Basis of Angular andDistance Measurements while Airborne (ALRFM).

For aero-terrestrial applications, a system is considered whichcomprises a sensor in motion operating with a tracking mode pursuing anobject of the scene. In this situation, along the whole of a trajectorythe system makes numerous measurements composed of positions of thesensor, of angular measurements of the LoS of the sensor and ofdistances from the sensor to the object of the scene.

Let us consider an ALRFM application seeking to estimate 2 angularbiases (Δψ, Δθ) and a distance bias (Δρ) with a sensor tracking a pointon the ground with unknown coordinates (x0, y0, z0) and its PRFMcounterpart when the distance measurement ρ is not available.

The way the observation equations are written makes it possible to writewhen simultaneously seeking the measurement biases and the position ofthe locked-on point on the ground (ALRFM) for example:

${\begin{pmatrix}1 & 0 & 0 & {\cos \; \psi_{k}\; \cos \; \theta_{k}} & {{- \rho_{k}}\; \sin \; \psi_{k}\; \cos \; \theta_{k}} & {{- \rho_{k}}\; \cos \; \psi_{k}\; \sin \; \theta_{k}} \\{0\;} & 1 & 0 & {\sin \; \psi_{k}\; \cos \; \theta_{k}} & {\rho_{k}\; \cos \; \psi_{k}\; \cos \; \theta_{k}} & {{- \rho_{k}}\sin \; \psi_{k}\; \sin \; \theta_{k}} \\{0\;} & 0 & 1 & {\sin \; \theta_{k}} & 0 & {\rho_{k}\; \cos \; \theta_{k}}\end{pmatrix}\begin{pmatrix}x_{0} \\y_{0} \\y_{0} \\\Delta_{\rho} \\\Delta_{\psi} \\\Delta_{\theta}\end{pmatrix}} = {\begin{pmatrix}x_{k} \\y_{k} \\z_{k}\end{pmatrix} + {\rho_{k}\begin{pmatrix}{\cos \; \psi_{k}\; \cos \; \theta_{k}} \\{\sin \; \psi_{k}\; \cos \; \theta_{k}} \\{\rho_{k}\; \sin \; \theta_{k}}\end{pmatrix}} + v_{k}}$

If it is desired to carry out calibration only, the coordinates of theground point may be deleted from the observation equations so as toreduce to the situations of PRFM and ARFM only calibration.

With 2 ensembles of measurements (x_(k), y_(k), z_(k), ψ_(k), θ_(k),ρ_(k)), as in FIG. 7 a, we have 6 equations which make it possible toexplicitly determine the position of the object and the measurementbiases. With a greater number of measurement ensembles, the above systemis simply solved, on account of its linearity, by least squares or byfiltering.

Application (3): Location and Calibration on the Basis of Positions andDistances

To calibrate measurement defects and have bias information of goodaccuracy, the overview of the system errors indicates that it isrelevant to establish a location of the object without using the angularmeasurements. In this application, we propose simultaneous estimation:

-   -   of the position of the object solely on the basis of the sensor        position measurements and of the distance measurements,    -   of the defects of distance measurement (bias and scale factor).

If desired, the knowledge of the estimated position of the object (onthe basis of the measurements corrected of their defect) allows angulardefects to be corrected a posteriori.

In the case of several distance measurements ρ_(k), carried out atpositions P_(k)(x_(k), y_(k), z_(k)), the defects in bias and in scalefactor may be estimated by keeping the sensor pointed at one and thesame object along the trajectory.

Thus, for a set of active measurements, exhibiting an error of biasb_(ρ), of scale factor s_(ρ) and measurement noise ν_(ρ), we seek tominimize the set of the following quantities:

δ_(n)=√{square root over ((x−x _(n))²+(y−y _(n))²+(z−z _(n))²)}{squareroot over ((x−x _(n))²+(y−y _(n))²+(z−z _(n))²)}{square root over ((x−x_(n))²+(y−y _(n))²+(z−z _(n))²)}−ρ_(n) −s _(ρ)ρ_(n) −b _(ρ)−ν_(ρ)

where (x, y, z) are the terrain coordinates of the point followed and(x_(n), y_(n), z_(n)) are the positions of the sensor for which ameasurement of the distance “d_(n)” separating the sensor from theobject is available. The defects of the telemeter (s_(ρ), b_(ρ), ν_(ρ))characterize respectively its scale factor, its bias and the measurementnoise.

In the LRFM approach, both the position of the object sighted and themeasurement defects are sought. The state vector consisting of theparameters to be estimated may be written:

Θ=[xyzb _(ρ) s _(ρ)]^(T)

u^(T) representing the transpose of the vector u.

In the RFM approach, the vector of parameters is reduced to the last 2components of the above vector.

In practice, a first approximate position of the object Θ₀ can beobtained by using all or some of the measurements assumed to bedefect-free. The following state vector is then obtained:

Θ₀ =[x ₀ y ₀ z ₀00]^(T)

The state vector of the system with the N measurements can then beobtained by a conventional iterative approach in the form:

Θ_(k)=Θ_(k−1)+ΔΘ_(k)

where:

ΔΘ_(k)=−(H ^(T) R ⁻¹ H)⁻¹ H ^(T)Σ⁻¹δ(Θ_(k−1))

with for N distance measurements an observation matrix H and theincrement in the vector of calibration components δΘ:

$H = {{\nabla_{\Theta}\delta} = \begin{pmatrix}\frac{x - x_{1}}{\rho_{1}} & \frac{y - y_{1}}{\rho_{1}} & \frac{z - z_{1}}{\rho_{1}} & {- 1} & {- \rho_{1}} \\\vdots & \vdots & \vdots & \vdots & \vdots \\\frac{x - x_{N}}{\rho_{N}} & \frac{y - y_{N}}{\rho_{N}} & \frac{z - z_{N}}{\rho_{N}} & {- 1} & {- \rho_{N}}\end{pmatrix}}$${\delta \left( \Theta_{k - 1} \right)} = \begin{bmatrix}{\delta_{1}\left( \Theta_{k - 1} \right)} \\\vdots \\{\delta_{N}\left( \Theta_{k - 1} \right)}\end{bmatrix}$

The matrix Σ represents the covariance of the measurement noise; itreduces to the product of the identity matrix times σ_(ρ) ² when themeasurements all have the same noise σ_(ρ) and when the noise values aremutually independent.

The application to particular trajectories demonstrates the ability ofthe scheme to simultaneously estimate the position of the object and themeasurement defects. To correctly estimate both the bias and the scalefactor on the distance, the configurations for which the distance to theobject does not remain constant are preferably chosen. Indeed, in thesituation where the distance to the object varies, the errorcontribution related to the scale factor does not behave as a bias andit is then possible to distinguish the two physical origins of thedefects.

Application (4): Calibration and Location by Aero-Lateration

Among the applications presented, this application represents the mostgeneral derivative in the sense that it makes it possible to correct in3D the georeferencing of the image by estimating the calibrationparameters while allowing for the following:

-   -   that the angular biases to be estimated exist in the three        directions in space,    -   that active measurements may or may not be used,    -   that a digital terrain model or a ground assumption is available        on the scene,    -   that the parameters to be estimated comprise contributions        relating to the internal parameters of the sensor,    -   that the parameters to be estimated do or do not comprise the        simultaneous location of object of the scene.

This method may be extended to other fixed objects G₁, G₂, . . . , inaddition to G₀. These other fixed objects must of course be visible onthe images or at least on some of them. They are preferably welldistributed around G₀ so as to have a more favorable estimationconfiguration. In this case the method comprises an additional step ofmatching one image with the other of these other objects, as a functionof the internal characteristics of the images. The latter depend on theinternal characteristics of the sensor which are assumed to be known;this entails:

-   -   for the detector: the resolution of the detector, the number of        rows and columns of the photosensitive matrix, and    -   for the optics: the focal length, the coordinates of the image        principal point and the distortion.

Utilizing several fixed points G₁, G₂, . . . on several images makes itpossible to estimate the measurement defects in the three degrees ofangular freedom: Δψ, Δθ and Δφ. The tracking and the distancemeasurements, if any, are carried out on the fixed point G₀ at thecenter of the images, and at least one other visible fixed point on theground of the sequence of images must be followed. In practice, severalobjects of the scene giving rise to points of interest are followedsimultaneously, thereby limiting the loss of observation when objectscome to leave the instantaneous field of vision of the sensor, soimproving the estimation result and the probability of having pointsbetter distributed over the whole image.

The calibration parameters are obtained by minimizing the followingexpression:

     Θ_(R) = min  χ²$\chi^{2} = {{v^{2}\left( \Theta_{R} \right)} + {v^{2}\left( \Theta_{Ii} \right)} + {\sum\limits_{i = 1}^{I}\left\lbrack {{v^{2}\left( \Theta_{Ei} \right)} + {v^{2}\left( \rho_{0i} \right)} + {v^{2}\left( A_{i} \right)} + {\sum\limits_{k = 1}^{K}{v^{2}\left( P_{ik} \right)}}} \right\rbrack}}$

where the quantities respectively represent the residuals in: thecalibration parameters, the picture-taking external parameters, theinternal (or intrinsic) parameters of the sensor, the distance at imagecenter, the coordinates, if any, the ground coordinates of pointscorresponding to the features, the features. By expressing this in moredetail:

$\mspace{79mu} {{v^{2}\left( \Theta_{R} \right)} = {\delta_{\Theta_{R}}^{T}{\sum_{\Theta_{R}}^{- 1}\delta_{\Theta_{R}}}}}$$\delta_{\Theta_{R}} = \begin{pmatrix}{\tau_{x} - \tau_{x}^{*}} & {\tau_{y} - \tau_{y}^{*}} & {\tau_{z} - \tau_{z}^{*}} & {ɛ_{x} - ɛ_{x}^{*}} & {ɛ_{y} - ɛ_{y}^{*}} & {ɛ_{z} - ɛ_{z}^{*}}\end{pmatrix}^{T}$$\mspace{79mu} {{v^{2}\left( \Theta_{Ii} \right)} = {\delta_{Ii}^{T}{\sum_{Ii}^{- 1}\delta_{Ii}}}}$$\delta_{I\; i} = \begin{pmatrix}{p_{0} - p_{0}^{*}} & {q_{0} - q_{0}^{*}} & {f_{0} - f_{0}^{*}} & {p_{c} - p_{c}^{*}} & {q_{c} - q_{c}^{*}} & {K_{1} - K_{1}^{*}}\end{pmatrix}^{T}$$\mspace{79mu} {{v^{2}\left( \Theta_{Ei} \right)} = {\delta_{Ei}^{T}{\sum_{Ei}^{- 1}\delta_{Ei}}}}$$\delta_{E\; i} = \begin{pmatrix}{x_{i} - x_{i}^{*}} & {y_{i} - y_{i}^{*}} & {z_{i} - z_{i}^{*}} & {\psi_{i} - \psi_{i}^{*}} & {\theta_{i} - \theta_{i}^{*}} & {\phi_{i} - \phi_{i}^{*}}\end{pmatrix}^{T}$$\mspace{79mu} {{v\left( \rho_{0\; i} \right)} = {\delta_{\rho_{0i}}^{T}{\sum_{\rho_{0\; i}}^{- 1}\delta_{\rho_{0\; i}}}}}$     δ_(ρ_(0 i)) = ρ_(0 i) − ρ_(0 i)^(*)     Λ_(ρ_(0 i)) = E[d_(ki)d_(ki)^(T)] = σ_(ρ)²$\mspace{79mu} {\rho_{0\; i} = \sqrt{\left( {x_{G\; 0} - x_{ki}} \right)^{2} + \left( {y_{G\; 0} - y_{ki}} \right)^{2} + \left( {z_{G\; 0} - z_{ki}} \right)^{2}}}$${v^{2}\left( A_{i} \right)} = {\begin{pmatrix}{x_{i} - x_{G}} & {y_{i} - y_{G}} & {z_{i} - z_{G}}\end{pmatrix}{\sum_{A}^{- 1}\begin{pmatrix}{x_{i} - x_{G}} & {y_{i} - y_{G}} & {z_{i} - z_{G}}\end{pmatrix}^{T}}}$$\mspace{79mu} {{v^{2}\left( P_{ik} \right)} = {\delta_{Pik}^{T}{\sum_{Pik}^{- 1}\delta_{Pik}}}}$$\mspace{79mu} {\delta_{Pik} = \left\lbrack {\begin{pmatrix}x_{Gk} & y_{Gk} & z_{Gk}\end{pmatrix} - {G\left( {\Theta_{i},p_{ik},q_{ik}} \right)}} \right\rbrack^{T}}$$\mspace{79mu} {\sum_{Pik}{= \begin{pmatrix}\sigma_{pik}^{2} & \sigma_{pq} \\\sigma_{pq} & \sigma_{qik}^{2}\end{pmatrix}}}$

The quantities Σ and σ represent the a priori covariances in theparameters.

The scheme for minimizing the criterion relies on a conventionaltechnique:

-   -   either of Newton type by processing the observations batch-wise,        starting from an initial solution, using the measurements logged        for the picture-taking parameters, the approximate knowledge of        the internal parameters of the sensor (if they have to be        estimated), and the fact that the values of the calibration        parameters are small i.e. Θ_(R)=(0,0,0,0,0,0)^(T) and then by        proceeding by iteration after linearization to minimize the        criterion. Each step provides an estimation of the differences        dΘ_(R), dΘ_(Ei), . . . which makes it possible to resume the        estimation from the initial step    -   or of Kalman type by processing the measurements on the fly,        that is to say by estimating the parameter vector in tandem with        the production of the matches between the images of the sequence    -   or by relaxation by estimating in a step No 1 the picture-taking        parameters, Θ_(Ei1), Θ_(R1,1) being assumed zero (no bias); and        then in a step No 2 by estimating Θ_(R1,2) on the basis of the        external parameters obtained in step 1. The estimation process        thereafter resumes from step No 1 with the value Θ_(Rn−1,2) of        the calibration parameters to obtain an ensemble of        picture-taking parameters Θ_(Ein), making it possible to        estimate Θ_(Rn,2); and so on, up to convergence.

Implementation of the Process and Optimization of Performance

To improve the performance in the estimations of the calibration and/orto provide support to the automatic management of the measurementinstrument and/or to the platform navigation function, it is proposed:

-   -   1) starting from a given trajectory (under flight plan), to seek        the ideal zone at which to point the sensor in order to carry        out the calibration,    -   2) starting from the position of an object on which the sensor        must carry out its calibration, to propose a trajectory making        it possible to approach the ideal estimation performance.

In detail, it is sought to improve the performance in the parametersestimated during calibration:

-   -   1) by adapting the trajectory for a sighted point. Accordingly,        future positions P₁, P₂, . . . which will optimize the        estimation performance are calculated starting from an initial        position P₀ and from a speed V₀. To carry out this optimization,        use is made of for example the Fisher information (FIM Fisher        Information Matrix) which quantifies the information relating to        the measurement ensembles with a view to the best possible        estimation of the bias. The interest therein lies in its        character of additivity, which makes it possible to aggregate        the information afforded by the trajectory up to the point P_(n)        with the various possibilities which may be envisaged at the        time T_(n+1). Starting from the measurement information and the        approximate knowledge of the position of an object on which to        calibrate, the aim of optimizing the trajectory is to achieve        better calibration performance than that which would be obtained        by following for example a pre-established flight plan. Starting        from an initial speed, it is proposed to call into question the        speed vector envisaged for the platform. This is carried out on        one step, in terms of spatial distance and heading, with an        amplitude compatible with the kinematic constraints of the        platform (according to admissible acceleration). Starting from a        current node, a set of nodes is then obtained, with the one        retained corresponding to the maximum value of a criterion of        the FIM (based on the trace or determinant or combination of the        eigenvalues). It is proposed to deal with each step in terms of        azimuth and then elevation.    -   2) by acting on the choice of the object G₀ to be sighted. For a        predefined trajectory (case of a platform under flight plan);        the agileness of the LoS of the measurement instrument is used        in such a way as to point at a zone in space which will produce        Fisher information of greatest worth for the fixed        characteristics of the trajectory and of the measurement (rate,        geometry and precision). Accordingly, a sampling is carried out        of the zone of the scene attainable to carry out the calibration        according to a spatial grid whose nodes bear the Fisher        information calculations. The object is thereafter chosen in the        zone corresponding to the node where the information is of        greatest worth. The decision to actually work on this zone can        thereafter be conditioned on the number, on the distribution and        on the contrast of the objects of interest detected by the        sensor when it is pointing at this zone.

For information corresponding to the measurements of the instant k, theFisher information matrices, mentioned hereinabove, take the followingforms:

FIM(k)=J _(k) ^(T)Λ_(k) ⁻¹ J _(k)  (equation 2)

where the matrices J and Λ representing the Jacobians and Covariances ofmeasurements may be written for the ALRFM and PLRFM calibration as:

${J_{ALRFM}(k)} = {\begin{bmatrix}\frac{\partial\Delta_{\rho}}{\partial x_{0}} & \frac{\partial\Delta_{\psi}}{\partial x_{0}} & \frac{\partial\Delta_{\theta}}{\partial x_{0}} \\\frac{\partial\Delta_{\rho}}{\partial y_{0}} & \frac{\partial\Delta_{\psi}}{\partial y_{0}} & \frac{\partial\Delta_{\theta}}{\partial y_{0}} \\\frac{\partial\Delta_{\rho}}{\partial z_{0}} & \frac{\partial\Delta_{\psi}}{\partial z_{0}} & \frac{\partial\Delta_{\theta}}{\partial z_{0}} \\\frac{\partial\Delta_{\rho}}{\partial\Delta_{\rho}} & \frac{\partial\Delta_{\psi}}{\partial\Delta_{\rho}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{\rho}} \\\frac{\partial\Delta_{\rho}}{\partial\Delta_{\psi}} & \frac{\partial\Delta_{\psi}}{\partial\Delta_{\psi}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{\psi}} \\\frac{\partial\Delta_{\rho}}{\partial\Delta_{\theta}} & \frac{\partial\Delta_{\psi}}{\partial\Delta_{\theta}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{\theta}}\end{bmatrix} = \begin{bmatrix}{- \frac{{dx}_{k}}{\rho_{k}}} & \frac{{dy}_{k}}{r_{k}^{2}} & {\frac{{dx}_{k}}{r_{k}}\frac{{dz}_{k}}{\rho_{k}^{2}}} \\{- \frac{{dy}_{k}}{\rho_{k}}} & {- \frac{{dx}_{k}}{r_{k}^{2}}} & {\frac{{dy}_{k}}{r_{k}}\frac{{dz}_{k}}{\rho_{k}^{2}}} \\{- \frac{{dz}_{k}}{\rho_{k}}} & 0 & {- \frac{r_{k}}{\rho_{k}^{2}}} \\1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}}$ ${J_{PLRFM}(k)} = {\begin{bmatrix}\frac{\partial\Delta_{\psi}}{\partial x_{0}} & \frac{\partial\Delta_{\theta}}{\partial x_{0}} \\\frac{\partial\Delta_{\psi}}{\partial y_{0}} & \frac{\partial\Delta_{\theta}}{\partial y_{0}} \\\frac{\partial\Delta_{\psi}}{\partial z_{0}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{0}} \\\frac{\partial\Delta_{\psi}}{\partial\Delta_{\psi}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{\psi}} \\\frac{\partial\Delta_{\psi}}{\partial\Delta_{\theta}} & \frac{\partial\Delta_{\theta}}{\partial\Delta_{\theta}}\end{bmatrix}_{k} = \begin{bmatrix}\frac{{dy}_{k}}{r_{k}^{2}} & {\frac{{dx}_{k}}{r_{k}}\frac{{dz}_{k}}{\rho_{k}^{2}}} \\{- \frac{{dx}_{k}}{r_{k}^{2}}} & {\frac{{dy}_{k}}{r_{k}}\frac{{dz}_{k}}{\rho_{k}^{2}}} \\0 & {- \frac{r_{k}}{\rho_{k}^{2}}} \\1 & 0 \\0 & 1\end{bmatrix}}$

The covariance matrices Λ are diagonal with on the diagonal the termsΛ_(ALRFM)=diag [σ_(x) ², σ_(y) ², σ_(z) ², σ_(ρ) ², σ_(ψ) ², σ_(θ) ²] inARFM and Λ_(PLRFM)=diag [σ_(x) ², σ_(y) ², σ_(z) ², σ_(ψ) ², σ_(θ) ²] inPRFM. In these expressions:

dx _(k) =x _(k) −x ₀=ρ cos ψ cos θ

dy _(k) =y _(k) −y ₀=ρ sin ψ cos θ

dz _(k) =z _(k) −z ₀=ρ sin θ

ρ_(k)√{square root over (r_(k) ²+(z _(k) −z ₀)²)}

r _(k)=√{square root over ((x _(k) −x ₀)²+(y _(k) −y ₀)²)}{square rootover ((x _(k) −x ₀)²+(y _(k) −y ₀)²)}

Evaluations carried out on several scenarios show that the estimation ofthe defects of bias (more precisely of their modulus) is favored withrectilinear trajectories going toward the point G₀ or passing by anobject G₀ situated nearly plumb with the trajectory.

Implementation of the Process with Variability of the ParametersEstimated According to Operating Conditions

In the various applications proposed, it is possible to introduce thevariability of the operating conditions in the modeling and estimationprocesses. Accordingly, the modeling introduces a dependency of theparameters on the thermomechanical conditions logged.

Thus when study of the system shows that the values of the calibrationparameter to be estimated are sensitive to the operating conditions,this parameter is modeled with a dependency on the thermomechanicalconditions. In a simple manner, use is made of a polynomial modelingwhich exhibits the advantage of preserving the linearity of the systemto be solved with regard to the parameters to be estimated. For examplethe evolution of the parameter “a” with temperature is written using afinite expansion, limited to order N, about a mean temperature of use T₀in the form:

${a(T)} = {\sum\limits_{n = 0}^{N}{a_{n}\left( {T - T_{0}} \right)}^{n}}$

By limiting the expansion to first order, the estimation of a₀ consistsin solving a system identical to the above, which is independent of thethermal conditions. To first order, measurement of the temperature Tallows the estimation of the coefficient a₁, the thermal drift of theparameter “a”.

In the proposed applications, the performances obtained in typicalscenarios are:

-   -   for the angles of mounting of the measurement instrument on the        platform, of the order of 1%₀ of their value;    -   for the biases of measurements of the order of a few % of their        value. This is for angular measurements provided by inertial        components, for distance measurements provided by a telemeter        and also for the scale factors existing in the magnitudes        measured.

Applied to location, this method makes it possible to maintaindecametric accuracy in location for recognition and designation ofobjectives on the ground in the presence of bias.

The proposed method may be implemented under the following conditions:

-   -   either in a supervised manner, in an approach to a zone of        interest, the supervisor of the airborne optronic system decides        to establish a calibration of the measurement system. It then        decides an appropriate zone (VC) in which the lock-on point G₀        is searched for. The point G₀ may be chosen by the supervisor        (as well as optionally the other points G₁, G₂, etc.),    -   or in an automatic manner, in a mode where the sensor is        available in the sense that it is not utilized for an        operational function. Having regard to the trajectory of the        aircraft, an appropriate zone is defined in which the lock-on        point G₀ is chosen automatically by an image processing which        searches for a contrasted point in this zone and optionally        verifies the presence of other points G₁, G₂, . . . , nearby.

The measured defects are optionally compared with the historical log ofthe previous evaluations and a current correction is evaluated. Thecorrection is applied to the following measurements of the measurementinstrument, obtained for example outside of this calibration method.

In a terrestrial system such as for example a portable camera, it ispossible by virtue of the method to locate a target by means of amagnetic compass and of a telemeter without having to estimate the localmagnetic declination. Accordingly, a characteristic ground point G₀ issighted, on which two ensembles of measurements from two differentpositions P₁, P₂ are carried out by displacing the camera. Thesepositions are for example provided by a positioning system such as aGPS. In this case the image acquisition device does not necessarilyrecord said images. In this form the correction makes it possible toevaluate the local declination and to utilize the information with aview to locating other points of the scene G₁, G₂, . . . , in a widezone around which the calibration took place.

An exemplary optronic system equipped with means for calibrating ameasurement instrument has been represented in FIG. 2.

It comprises:

-   -   a device 10 for acquiring images of a scene comprising a fixed        object G₀; this device for acquiring images does not necessarily        record said images;    -   manual or automatic means 15 for tracking the fixed object G₀        during the acquisition of these images;    -   at least one instrument for measuring the distance 25 and/or one        instrument for measuring angles of orientation and/or of        attitude 30 between this measurement instrument and the fixed        object G₀, according to a line of sight LoS. This instrument has        to be calibrated;    -   positioning means 20 able to provide the positions P₁, P₂, . . .        P_(i), . . . , P_(j), . . . of the system,    -   a device 41 for rectification and synchronization of the        measurements with these positions. The rectification consists in        particular in applying the corrections estimated by the        calibration process,    -   a calculation unit 40 able to estimate the measurement defects        which minimize the dispersion of at least two points of        intersection G_(ij) between the LoS at the position P_(i) and        the LoS at the position P_(j), as a function of said        measurements and of the positions P_(i), P_(j) of the system and        able to apply the estimated defects to the measurements.

1. A method for calibrating measurement instruments of an optronicsystem in motion, with positions P₁, P₂, . . . , P_(i), . . . , theoptronic system-comprising a device for acquiring images of a scenecomprising a fixed object G₀, and means for tracking the fixed object G₀during the acquisition of these images, means for obtaining thepositions P₁, P₂, . . . , at least one instrument for measuring thedistance and/or an instrument for measuring angles of orientation and/orof attitude between this measurement instrument and the fixed object G₀,according to a line of sight LoS, wherein the method comprises thefollowing steps: acquisition at instants t₁, t₂, . . . of at least twoimages, each image being acquired on the basis of different positionsP₁, P₂, . . . of the system, the fixed object G₀ being sighted in eachimage, but its position being unknown, acquisition at the instants t′₁,t′₂, . . . of measurements of distance and/or of angle, synchronizationof the measurements of distance and/or of angle with the positions P₁,P₂, . . . established at instants t₁, t₂, . . . , estimation of themeasurement defects which minimize the dispersion of at least two pointsof intersection G_(ij) between the LoS at the position P_(i) and the LoSat the position P_(j), as a function of said measurements and of theknown positions P_(i), P_(j) of the system.
 2. The calibration method asclaimed in claim 1, wherein G₀ is at the center of the images.
 3. Thecalibration method as claimed in claim 1, wherein the sole calibratedmeasurement instrument is an instrument for measuring angles oforientation and/or of attitude, and the measurements are acquired on thebasis of at least three different positions P₁, P₂, P₃.
 4. Thecalibration method as claimed in claim 1, wherein the sole calibratedmeasurement instrument is a telemeter, and the measurements are acquiredon the basis of at least two different positions.
 5. The calibrationmethod as claimed claim 1, wherein, at least one other fixed object G₁being visible on at least two images, it furthermore comprises a step ofmatching in each image of the fixed objects G₀, G₁, the step ofcalculating the measurement defects furthermore being carried out as afunction of predetermined characteristics internal to the imageacquisition device.
 6. The calibration method as claimed in claim 1,further comprising optimizing the measurement conditions which is basedon the determination of an optimal trajectory of the sensor for a knownposition of the object G₀, or on the determination of a zone to befavored for the search for the object G₀.
 7. The calibration method asclaimed claim 1, further comprising calculating the geographicalposition of G₀ and optionally of the other fixed objects, on the basisof the calibrated measurements.
 8. The calibration method as claimed inclaim 1, further comprising pointing at the fixed object G₀.
 9. Thecalibration method as claimed in claim 1, further comprising applyingthe estimated defects to the distance measurement instrument and/or tothe instrument for measuring angles of orientation and/or of attitude soas to benefit from corrected measurements.
 10. An optronic system ableto be displaced, which comprises: a device for acquiring images of ascene comprising a fixed object G₀, and means for tracking the fixedobject G₀ during the acquisition of these images, means for obtainingthe positions P₁, P₂, . . . at least one instrument for measuring thedistance and/or one instrument for measuring angles of orientationand/or of attitude between this measurement instrument and the fixedobject G₀, according to a line of sight LoS, further comprising meansfor implementing the method as claimed in claim 1.